SIAM Journal on Scientific Computing, Volume 42, Issue 2, Page B520-B547, January 2020.
In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity, the oscillations generated by the stiff term are periodic. The homogenized model is then derived, and several state-of-the-art multiscale methods, in combination with the particle-in-cell discretization, are proposed for solving the Vlasov--Poisson equation. Their accuracy as much as their computational cost remain essentially independent of the strength of the magnetic field. The proposed schemes thus allow large computational steps, while the full gyro-motion can be restored by a linear interpolation in time. In the linear case, extensions are introduced for a general magnetic field (varying intensity and direction). Eventually, numerical experiments are exposed to illustrate the efficiency of the methods and some long-term simulations are presented.

中文翻译：

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强磁场变化方向下三维Vlasov方程的一致精确方法

SIAM科学计算杂志，第42卷，第2期，第B520-B547页，2020年1月。
在本文中，我们考虑具有不均匀，变化方向，强磁场的三维Vlasov方程。只要磁场强度恒定，刚度项所产生的振荡就是周期性的。然后推导出均质化模型，并提出了几种最新的多尺度方法，并结合了单元中粒子离散化技术来求解Vlasov-Poisson方程。它们的准确性以及计算成本基本上与磁场强度无关。因此，所提出的方案允许大量的计算步骤，而可以通过及时的线性插值来恢复完整的陀螺运动。在线性情况下，引入了针对一般磁场（强度和方向变化）的扩展。最终，